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In-s [12.5K]
3 years ago
7

A street light is at the top of a 10 ft tall pole. A woman 6 ft tall walks away from the pole with a speed of 8 ft/sec along a s

traight path. How fast is the tip of her shadow moving when she is 40 ft from the base of the pole?

Physics
1 answer:
Citrus2011 [14]3 years ago
5 0

Answer:

the shadow is moving with 12ft/s from the woman

Explanation:

let the distance from the pole to the shadow tip be L

\frac{10}{6} = \frac{L}{x}

L=\frac{5}{3}x

\frac{\mathrm{d} (QR)}{\mathrm{d} t}= 8ft/s

\frac{\mathrm{d} (L-x)}{\mathrm{d} t}= 8ft/s

\frac{\mathrm{d} (L)}{\mathrm{d} t}-\frac{\mathrm{d} (x)}{\mathrm{d} t}= 8ft/s

\frac{\mathrm{d} (L)}{\mathrm{d} t}=\frac{5}{3}\frac{\mathrm{d} (x)}{\mathrm{d} t}

\frac{\mathrm{d} (x)}{\mathrm{d} t}=12ft/s

\frac{\mathrm{d} (L)}{\mathrm{d} t}=16ft/s

hence the shadow is moving with 12ft/s from the woman

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